## Projects

Gesture Enhancement of Virtual Agent Mathematics Tutor

 This project seeks to build and evaluate an embodied-agent based mathematics learning environment that supplements tutorial interaction with gestures that are realistically executed as well as naturalistically timed vis-à-vis students’ multimodal actions and speech contributions. The design will seamlessly integrate the Mathematical Imagery Trainer, an empirically researched embodied-learning device, with a gesturing pedagogical agent. Through designing gesture-generation algorithms that are deeply grounded in gesture and learning research, we hope to significantly improve the performance of pedagogical agents in the mathematics domain, while also developing general guidelines for generating agent gesture. [read more]

"Kinemathics": Kinetically Induced Mathematical Learning

 Since the Fall of 2008 we have been developing and researching mathematics learning activities centered on a new form of interactive educational technology a system we call the Mathematical Imagery Trainer. We ask children to manipulate virtual objects on a computer screen to make the screen green and keep moving the hands all the while keeping the screen green. The children learn to move in a new way and then they describe this motion. The descriptions become mathematical discourse expressing new concepts. [read more]

Seeing Chance: Fostering Student Implicit Knowledge Towards Fluency in the Domain of Probability and Statistics

 The project evalauted new activities for the teaching and learning of probability. The activities were designed to enable students to bridge naive and analytical visualizations of a randomness experiment. Materials included a bin of marbles and scooper as the random generator, resources for combinatorial analysis, and computer-based simulations of the same experiment. We worked with students in Grades 4-6 as well as with 7th graders and undergraduate and graduate students. Across the gamut, all students used the same form of perceptual judgment when looking at the situation in non-analytical ways but were challenged by the rationale of the formal analysis for the experiment. The challenge, it turned out, centered on how they were seeing specific outcomes in the sample space, what sense they made of these objects. Much of the publications coming from this project focus on how the students were guided to recognize and negotiate competing visualizations of one and same object, and how that cognitive and social process was resolved as learning. [read more]

Giant Steps for Algebra

 GS4A is a design-based research project investigating the cognittion, teaching, and learning of early aglebra. The project is centered on a technology-based activity, in which students use computer-interface resources so as to model a narrative about a giant burying stolen treasure on a desert island. The idea is for students to 're-invent' the basic principles of algebraic thinking, and in particular solving a system of two story-equations. This work led to developing a design construct we call "reverse scaffolding." This means that rather that a teacher offering support that then fades out, it is the child who initiates and builds new mathematical functions that then fade in. By 'fade in' we mean that the computer takes over enacting those functions, thus freeing up the child to work on higher-order issues. Another new construct that emerged from this project is that of a SILO -- situated intermediary learning objective -- which attempts to capture a proto-conceptual type of practical knowledge about how to organize information toward solving a problem. This work built on ideas coming from constructionism as well as the related idea of transparency. Our various publications explain the rationale, early work, results from the main study, and reflections on the design process. [read more]

### Previous Projects

 In the PDMPS project, we designed, implemented, and evaluated an experimental curriculum for pre-service teachers and future education researchers enrolled in graduate-level college courses on mathematics cognition, learning, and instruction. Central to this design are selected 'paradigmatic didactical-mathematical problematic situations,' i.e., unique activities evoked as contexts for collaborative inquiry into the epistemology, pedagogy, and practice of mathematics as well as into subject matter content. [read more]

The Real World as a Trick Question: Mathematical Modeling, Knowledge, and Assessment

 Study consisted of conducting and analyzing probability-related clinical interviews with college students majoring in statistics to explore issues of intuitive reasoning. 24 undergraduate/graduate students enrolled in mathematical programs participated in one-to-one interviews as part of a design-based research study of the cognition of probability. I argue for the utility of guided, situated problem solving for the learning and consolidation of probability concepts. [read more]

Handing Down Mathematics: The Roles of Gesture in Design, Teaching, and Learning

 Analyzing videotaped classroom interactions to understand the roles of gesture in the design, teaching, and learning of mathematics. [read more]

Distributed Learning in Practice and Theory
 Tackling distributed-learning theoretical models from a complexity-studies perspective to frame the design and implementation of agent-based models and their extensions that support participatory simulations in mathematics classrooms; Using agent-based modeling to study and develop theoretical models of group learning. [read more]

The Three M's: Imagination, Embodiment, and Mathematics

 Research into the mechanisms and potential role of imagination in mathematical reasoning. [read more]

Fractal Village

 Design-based research utilizing a critical and constructionist pedagogical philosophy in an alternative high school setting to study mathematical agency, computational literacy, and identity. [read more]

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